Sobol and GJR-GARCH for Dominant Factors of European Option Prices in Blue-Chip Index Constituent Stocks

Abstract

Conditional volatility-based option pricing research generally emphasizes improving volatility inputs, but has not yet fully explained the relative contribution of each parameter to variation in simulated option-pricing responses for Indonesian index stocks. This study integrates Black–Scholes, GJR-GARCH asymmetric volatility, and Sobol global sensitivity analysis to identify dominant factors in a model-generated European call-option response for verified constituents of an Indonesian blue-chip index, denoted Index X. The sample consists of 19 constituents that remained consistent from February 2022 to December 2025. Logarithmic returns are tested for stationarity and ARCH effects, conditional volatility is estimated using GJR-GARCH(1,1), and the Black–Scholes response is evaluated with five independently and uniformly distributed inputs: moneyness, maturity, risk-free rate, volatility multiplier, and proportional transaction cost. The results show that all returns are stationary and most stocks exhibit significant ARCH effects. Under the baseline domain, maturity and moneyness are the leading factors, while the volatility multiplier is secondary and the risk-free rate and transaction cost have smaller contributions. The ranking remains contract-dominated under a wider scenario domain and under a Student-t innovation check, although the magnitudes and ordering of maturity and moneyness can change. The contribution of this research is sensitivity decomposition of a specified Black–Scholes response with a GJR-GARCH-based volatility input, not evidence of improved pricing accuracy against observed option prices. Issuer and index identities are masked in the manuscript to prevent issuer-specific model outputs from being misconstrued as investment recommendations or comparative assessments; a confidential identity crosswalk is retained for editorial verification.